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Theorem sbhypf 2735
 Description: Introduce an explicit substitution into an implicit substitution hypothesis. See also csbhypf . (Contributed by Raph Levien, 10-Apr-2004.)
Hypotheses
Ref Expression
sbhypf.1
sbhypf.2
Assertion
Ref Expression
sbhypf
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)   ()

Proof of Theorem sbhypf
StepHypRef Expression
1 vex 2689 . . 3
2 eqeq1 2146 . . 3
31, 2ceqsexv 2725 . 2
4 nfs1v 1912 . . . 4
5 sbhypf.1 . . . 4
64, 5nfbi 1568 . . 3
7 sbequ12 1744 . . . . 5
87bicomd 140 . . . 4
9 sbhypf.2 . . . 4
108, 9sylan9bb 457 . . 3
116, 10exlimi 1573 . 2
123, 11sylbir 134 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331  wnf 1436  wex 1468  wsb 1735 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688 This theorem is referenced by:  mob2  2864  cbvmptf  4022  tfisi  4501  ralxpf  4685  rexxpf  4686  nn0ind-raph  9168
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